1

Advances for a Solenoid/Dipole 6D Cooling Ring

X. Ding, UCLA

Muon Accelerator Program-Winter MeetingJefferson Lab

3/1/11

2

Collaborators

• D. Cline (UCLA)

• Al. Garren (PBL)

• H. Kirk (BNL)

• J. S. Berg (BNL)

X.Ding3/1/11

3

Outline

1. Evolution of the Solenoid/Dipole Ring

Cooler Design

2. Analysis of lattices (Beam Dynamics)

3. 6D Cooling

4. Summary

X.Ding3/1/11

Evolution of the Solenoid/Dipole Ring Cooler(Racetrack Lattice)

4X.Ding3/1/11

Evolution of the Solenoid/Dipole Ring Cooler(Problem with the Racetrack Lattice)

• Excessive losses in lattice• Low working momentum (145 MeV/c): large

dispersion• Very limited energy acceptance• Strong transverse/longitudinal couping• Non-robust cooling rate

3/1/11 X.Ding 5

6

DipoleSolenoid

Evolution of the Solenoid/Dipole Ring Cooler(Four-sided Lattice)

X.Ding3/1/11

Evolution of the Solenoid/Dipole Ring Cooler(Switch from racetrack to 4-sided)

• Reduce dispersion

• High energy operation: XZ partition numbers improved

• Improve dynamic aperture

• Achieve robust 6D cooling

3/1/11 X.Ding 7

8

Racetrack ring 4 sided ring 4 sided ring(modified)

Momentum 145 MeV/c 145 MeV/c 145 MeV/c

Superperiods 2 4 4

Arc length 6 m 7 m 6 m

Straight section length 5.85 m 5 m 5 m

Superperiod length & xytunes

11.85 m, 1.748 12 m, 1.75 11 m, 1.75

Circumference 23.7 m 48 m 44 m

Evolution of the Solenoid/Dipole Ring Cooler

(Specifications)

X.Ding3/1/11

Analysis of Lattices(Racetrack: Left, 4-sided: Right)

Dispersion is reduced in the 4-sided cooling ring

3/1/11 X.Ding 9

10

Analysis of Lattices

X.Ding3/1/11

Time of Flight minimum for the 4-sided lattice moves to higher energy and it can increase lattice energy

11

Analysis of Lattices Dynamic Aperture (4-sided Lattice)

X.Ding3/1/11

6D Cooling (4 sided ring)

Layout of RF Cavity & LH2 Absorber in a 4-sided ring quadrant

B

SOL+ SOL- SOLS+ SOLS-

o o 2oo o o oo +os 2os oosoos 2os oo+os o o 2 oo o o 2oo

SOLS+ SOLS- SOL- SOL+LH2

RF RFLH2

RFRF

12X.Ding3/1/11

Accelerating gradient, RF phase and frequency

15 MV/m, 30 degree,201.25 MHz

Length and energy loss rate in the LH2 wedge absorber

19.5cm, 0.3 MeV/cm

13

6D Cooling (4 sided ring)Cold Beam -- Equilibrium

(LH2-Wedge/23 deg, with Stochastics)

X.Ding3/1/11

14

6D Cooling (4 sided ring)Damping without Stochastics

(LH2-Wedge/23 deg)

X.Ding3/1/11

15

6D Cooling (4 sided ring)

6D Cooling with Stochastics (LH2-Wedge/23 deg)

X.Ding3/1/11

16

6D Cooling (4 sided ring)

6D Cooling with Stochastics (LH2-Wedge/23 deg)

Number of turns 0 15 Reduction

Normalizes Horizontal emittance (mm) 6.97 4.955 1.4067

Normalized Vertical emittance (mm) 10.62 4.319 2.459

Normalized Longitudinal emittance (mm) 20.12 6.749 2.981

6D emittance (mm3) 1489.3 144.4 10.3

Transmission (%) 100 39.0

X.Ding3/1/11

6D Cooling (Modified 4-sided Lattice)

3/1/11 X.Ding 17

4 sided lattice

Modified 4 sided lattice

6D Cooling (Modified 4-sided Lattice)Cold Beam -- Equilibrium

(LH2-Wedge/23 deg, with Stochastics)

3/1/11 X.Ding 18

Transmission is much improved

6D Cooling (Modified 4 sided ring) 6D Cooling with Stochastics

(LH2-Wedge/23 deg)

3/1/11 X.Ding 19

6D cooling is much improved and transmission is higher for the modified 4 –sided lattice

6D Cooling (Modified 4 sided ring) 6D Cooling with Stochastics

(LH2-Wedge/23 deg)

3/1/11 X.Ding 20

Number of turns 0 15 Reduction

Normalizes Horizontal emittance (mm) 12.59 5.338 2.36

Normalized Vertical emittance (mm) 14.98 3.911 3.83

Normalized Longitudinal emittance (mm) 21.77 8.489 2.56

6D emittance (mm3) 1489.3 144.4 23.2

Transmission (%) 100 65.8

Summary

• The achromat lattices of the Dipole/Solenoid Ring Coolers are designed.

• The analysis of the lattices for their linear parameters and dynamic aperture are performed.

• The simulation demonstrates that our modified four sided ring cooler has a robust 6D cooling.

3/1/11 X.Ding 21